Hybrid Propagation and Control of Network Viruses on Scale-Free Networks

In the era of Internet of Everything and Big Data, network viruses have posed a major threat to modern society and thus how to accurately model and effectively suppress its spreading has been a major concern in the domain of complex networks and cybersecurity. To investigate the propagation of network viruses under the combined influence of network topology and vertical propagation, we propose a novel model of virus propagation in scale-free networks. Through rigorous qualitative analysis, the propagation threshold $R_0$ determining whether the virus in a network tends to extinction or not is figured out. Based on the proposed dynamical model, we explore the problem of how to dynamically contain the spread of malware with limited resources. By utilizing optimal control theory, the original malware containment problem is reduced to the optimal control problem of finding a blocking strategy which dynamically adjusts the blocking rate of external devices such that the accumulative cost is minimized. Moreover, we prove the existence of an optimal blocking strategy, followed by deriving an optimal system to support its numerical calculation. The correctness and effectiveness of involved theoretical findings are verified through a set of representative simulation experiments